The invention relates to a system for determining the topography of a curved surface, comprising a device for projecting patterns of lines on the surface to be examined, a detector device for registration of the image formed on the surface. Such systems are used, inter alia, in the case of the so-called keratometer for determining the external shape of the human eye, in particular the curvature of the external surface of the cornea, for example for measuring for contact lenses and accurately determining the topography of the cornea before and after surgery.
These systems can also be used in manufacturing and checking curved objects.
With the known commercially available photokeratometer the radius of curvature of the cornea is measured locally by comparing mirrored measurement figures on the interface between air and lacrimal fluid with test figures.
Places of equal slope can be mapped in this way. In the interpretation of such registrations, without previous knowledge of the object, errors cannot be ruled out. Only a limited area of the cornea is measured.
Unequivocal registrations of the topography of the surface of the cornea can be obtained with the keratometer of the type which is described in an article by Tetsuo Kawara, "Corneal topography using moire contour fringes", in Applied Optics, Vol. 18, pp. 3675-3678 (Nov. 1979). Such a keratometer makes use of moire contour lines, which are lines of equal height. For this purpose, the reflecting surface of the cornea is transformed into a perfectly diffusely radiating surface, through the application of a fluorescein film, as is necessary for said moire technique. The fluorescent light of the fluorescein film is used to form the image, while the excitation light (which through specular reflection could distort the image) of the projection device, consisting of a single projector, is filtered out. In order to achieve the accuracy for a spherical surface which he claimed, Tetsuo Kawara used a grating with approximately 12 line pairs per millimeter (lp/mm) which, because of a narrow slit-shaped diaphragm in the projection device having optical compensation for the slanting projection angle relative to the viewing axis of the keratometer and a small enough diaphragm of the camera with the required depth of field, forms an image on the reference grating of the camera.
Due to the slanting projection angle, the camera "sees" a superimposed pattern of a projected grating slightly deformed by the convex cornea and the reference grating. The spatial beat between the gratings, which becomes visible as an interference phenomenon, is known as moire. This interference image represents lines of equal height. Since in this moire arrangement a multiplication contrast is obtained, the height lines can be read directly from the photographs. Translation of these height lines into three meridional profiles produces information on the local radius of curvature of the cornea.
A serious general limitation of the moire projection system described is that, on the one hand, sufficient depth of field is required, for which a small diaphragm is needed, while, on the other hand, the height contour interval must be as small as possible, which only a grating with a large number of lp/mm can provide. The system described by Tetsuo Kawara is therefore diffraction limited. A higher resolution can be obtained only at the expense of the depth of field, or by increasing the projection angle of the grating relative to the optical axis of the camera. With a small depth of field the whole cornea is not mapped in one exposure,and a larger projection angle than approximately 18.degree. produces an image which can no longer be interpreted visually, on account of the occurrence of optical artifacts. In the case of the instrument described the height lines are displayed at the position of the reference grating instead of being located on the surface to be registered, which means that the flexibility of the instrument with regard to variation of image scale and image angle is low. The sign of the slope is not known (from previous knowledge is derived as "convex"). The product of Tetsuo Kawara's keratometer is a photograph. The translation of the height lines thus recorded into local radius of curvature, eccentricity etc. has to be carried out from there.
The dependence on very fine gratings in order to keep the moire contour interval (=measuring point) limited, could be removed in principle if, instead of the intensity distribution of the moire image, the local phase of the projected grating were used as the measuring point.
Moire height lines of a surface of an object are formed by the relative phases between the projected grating and the reference grating. The height lines will shift due to shifting of one of the gratings, with the result that a continuous phase measurement at one measuring point is possible. The intensity variation is then a measure of the phase variation. The measuring sensitivity and the accuracy then increase greatly. Since the movement device of the moving grating is known, the sign of the slope can be determined. In the case of the keratometer, on account of unavoidable eye movements, it is hardly possible to carry out such a dynamic measurement.
However, in the examination of surfaces of other objects, such as dentures, the use of a device is known from an article by F. H. M. Jongsma e.a.. "Real-time contouring of tooth imprints", in SPIE, Vol. 492, pp. 500-506, ECOOSA 1984, in which two interference patterns are projected at an angle relative to each other by means of an interferometer. Planes which are at right angles to the bisectrix of the angle and are alternately diffusely illuminated or contain more or less highly contrasting line patterns are thereby produced in the space in which the two light beams intersect. The distance between these parallel planes is equal and depends on the angle between the light beams and the distance between the lines in the projected grating pattern. If an object is now placed in this space, it alternately intersects the diffusely illuminated planes and the planes with the images of the grating pattern. As a result of this, intersection lines become visible on the object, which lines have a constant height difference from each other, although due to the summation effect the contrast of the two intensities is very low. In order to make said height lines visible, a spatial (optical) or temporal (electronic) filtering such as that described in above article by Jongsma c.s. must therefore still be used.
A disadvantage of moire images is that it is not possible to determine the sign of the slope other than from previous knowledge of the object. One method of overcoming this problem is described in French patent application No. 2,292,213 of 21 Nov. 1974. This patent application describes a method in which two moire projections are compared with each other. These moire registrations are produced in such a way that the reference plane of the second moire registration is displaced over a distance which is smaller than half the moire contour distance. Double contours with alternating small and larger intervals are thus produced. The contours are labelled with a colour, for example by making use of a yellow and a blue grating. The result is then a colour registration with the relatively small contour intervals yellow - blue or blue - yellow. The information of the sign of the slope is contained in the combination of distance and colour.
Another form of colour labelling is described in German patent application No. P 40 175 028 of 9 Mar. 1990. This patent application describes how two gratings of different colours are projected simultaneously on the object from different angles. The two gratings in the detection system can be processed separately by means of a colour separation mirror. The angle and the orientation of the slope relative to the sensor can then be calculated from the local spatial grating frequency on the object. What is essential in this system is the mechanical linking of the two gratings lying in one plane, so that their phase relation is fixed. As a result of this, by displacement of the gratings the noise can be averaged, while the height contours do not change position.
If unambiguous external shape information on the moist and reflecting surface of the cornea is desired, use can be made of the fluorescence technique described in the article by T. Kawara, in order to convert this reflecting surface into a Lambertian radiator. In these conditions, when there is a well-defined illumination, the local emission can then be calculated. In order to obtain a moire contrast, use can be made of the projection technique known from an article by J. Wasowski, "Moire topographic maps", in Opt. Communications, Vol. 2, pp. 321-323, 1970, by means of a projector of the type described by Kawara. If lasers which are suitable for this are available, it is also possible to choose the interferometer described by Wasowski as the grating producer, or another interference system can be used.